One-dimensional diffusions
3-4 hours of lectures per week.
Lecturer
Goran Peskir
Content
Strong markov processes with continuous sample paths are called diffusions. The main examples of diffusions are the Wiener process and the Ornstein-Uhlenbeck process. These processes are initially used to model physical Brownian motion. Subsequently a large number of other phenomena ranging from physics and biology to economics and finance are also modeled by diffusion processes. Presently diffusion processes play a central role in modern probability theory and its applications. Common to all diffusion models is that a probabilistic problem stands in one-to-one correspondence with a second-order differential problem satisfying boundary conditions. The aim of the course is to introduce basic definitions and concepts of one-dimensional diffusion processes and derive some key results of interest in theory and applications. The contents include:
1. The Wiener process
2. The ornstein-Uhlenbeck process
3. One-dimensional diffusions
4. The infinitesimal operator
5. The Kolmogorov forward and backward equations
6. Boundary classification
7.Further examples and problems
Prerequisites
Stochastic processes (the course can be followed independently of the course
Discrete Markov processes..
Literature
Lecture notes.
Evaluation
Active participation.
ECTS-credits
5.
Quarter
1st quarter of the spring term 2004.